Countable T-groups and von Neumann algebras

Factors with countable fundamental groups are investigated in connection with representations and actions of discrete with the property T. An example of an ICC-group is given, whose group factor has a countable fundamental group and a continuous locally compact group of outer automorphisms. In addition, for this factor all the tensor powers are mutually nonisomorphic. It is proved that there exists a continuum of nonisomorphic full factors of type III1 with a fixed Connes invariant Sd.